Question

Let $f:\mathbb{C}\rightarrow \mathbb{C}$ be the map given by $f(z)=\sin z-z$. Then image of $f$ is $\mathbb{C}$. (T/F)

score 70 · Answer 1 · 2026-04-08 03:50:14

70

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Let $f:\mathbb{C}\rightarrow \mathbb{C}$ be the map given by $f(z)=\sin z-z$. Then image of $f$ is $\mathbb{C}$. (T/F)

Published on 08 Apr 2026 - 3:50

score 125 · Answer 2 · 2026-04-12 18:42:32

125

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Evaluating $J_0(z)=\frac{1}{\pi}\int_{0}^{\pi}\cos\left(z\sin\theta\right)\,d\theta$

Published on 12 Apr 2026 - 18:42

score 71 · Answer 3 · 2026-04-13 12:04:37

71

Views

Computing an upper bound in the complex plane

Published on 13 Apr 2026 - 12:04

score 77 · Answer 4 · 2026-04-13 10:40:19

77

Views

Proving continuity in the complex plane using sequences

Published on 13 Apr 2026 - 10:40

score 74 · Answer 5 · 2026-03-26 12:36:29

74

Views

lower bound for absolute value of lambert series, Stein and Shakarchi pg 68

Published on 26 Mar 2026 - 12:36

score 42 · Answer 6 · 2026-04-11 10:02:54

42

Views

How to compute this integral involving trig?

Published on 11 Apr 2026 - 10:02

score 866 · Answer 7 · 2026-03-26 11:03:45

866

Views

Conformal mapping of region between two circles

Published on 26 Mar 2026 - 11:03

score 94 · Answer 8 · 2026-03-27 23:23:29

94

Views

Show that $\int_{-\infty}^{\infty}\exp\left({-\left(\sqrt {4\pi^{2} t}\xi+\frac{i(y-x)}{2\sqrt t}~\right)^{2}}\right)\,d\xi =\frac{1}{\sqrt {4\pi t}}$

Published on 27 Mar 2026 - 23:23

score 77 · Answer 9 · 2026-04-06 17:02:37

77

Views

Can one extend/derive definition of holomorphic complex function on a fragment of domain uniquely by analytic continuation

Published on 06 Apr 2026 - 17:02

score 33 · Answer 10 · 2026-04-09 04:48:57

33

Views

Solution of an equation involving complex numbers

Published on 09 Apr 2026 - 4:48

score 46 · Answer 11 · 2026-04-13 10:04:04

46

Views

Where is the flaw in my method of solving complex power series?

Published on 13 Apr 2026 - 10:04

score 466 · Answer 12 · 2018-03-01 17:01:02

466

Views

Prove Picard's theorem for $f(\zeta)=e^{1/\zeta}$.

Published on 01 Mar 2018 - 17:01

score 85 · Answer 13 · 2018-03-01 17:16:48

85

Views

Proving this polynomial is identically zero, as a result of this contour integration

Published on 01 Mar 2018 - 17:16

score 44 · Answer 14 · 2026-04-12 19:53:59

44

Views

Showing this inequality as a result of Cauchy's theorem

Published on 12 Apr 2026 - 19:53

score 42 · Answer 15 · 2018-03-01 19:07:57

42

Views

Angle-perserving map is holomorphic and has non-zero derivative

Published on 01 Mar 2018 - 19:07

List Question

Let $f:\mathbb{C}\rightarrow \mathbb{C}$ be the map given by $f(z)=\sin z-z$. Then image of $f$ is $\mathbb{C}$. (T/F)

Evaluating $J_0(z)=\frac{1}{\pi}\int_{0}^{\pi}\cos\left(z\sin\theta\right)\,d\theta$

Computing an upper bound in the complex plane

Proving continuity in the complex plane using sequences

lower bound for absolute value of lambert series, Stein and Shakarchi pg 68

How to compute this integral involving trig?

Conformal mapping of region between two circles

Show that $\int_{-\infty}^{\infty}\exp\left({-\left(\sqrt {4\pi^{2} t}\xi+\frac{i(y-x)}{2\sqrt t}~\right)^{2}}\right)\,d\xi =\frac{1}{\sqrt {4\pi t}}$

Can one extend/derive definition of holomorphic complex function on a fragment of domain uniquely by analytic continuation

Solution of an equation involving complex numbers

Where is the flaw in my method of solving complex power series?

Prove Picard's theorem for $f(\zeta)=e^{1/\zeta}$.

Proving this polynomial is identically zero, as a result of this contour integration

Showing this inequality as a result of Cauchy's theorem

Angle-perserving map is holomorphic and has non-zero derivative

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